United States Patent Publication 2007009469 teaches the use of a tray substrate and a flooring component to create a floating tile structure. The trays interlock with each other as demonstrated in FIG. 17 of that specification. U.S. Pat. No. 7,197,855 teaches the use of a tray substrate and a flooring component interlocked as well.
Both of these systems require that flooring components are laid in substantially the same direction and trueness. For example, the edges of the square of one substrate would interlock at the edges of the square of the other tray substrate. Neither of these systems provide any guidance on placing a specially shape tile, known as a medallion, in the middle of the interlocking pattern.